I presume you're referring to that part at the end of the Sister Sledge clip, where the final lyric "Sing" is reverb faded out.
To achieve something like this in Audacity, you'd first need to sample a portion of the song that you'd like to use, taking into account extra room for any fade-in and fade-out that you require.
To add the reverb effect, you'd select/highlight only the final part of the clip where you hear the lyric 'Sing' and apply reverb to that. Trying previewing with different amounts of Dry/Wet mix (so it doesn't get exaggeratedly louder/quieter). Also make sure you adjust the length of the reverb time so you can apply a good fade out. Then apply the reverb effect, your clip should increase in length due to the reverb.
Sometimes the reverb will fade-out exactly how you want, or you can apply a volume fade-out to the end of the clip to make it happen sooner if required.
That's pretty much all there is to it, you just need to practice playing with the reverb controls to get the desired effect, that just comes with experience.